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Here is problem 3.15 from Hyat: Engineering Circuit Analysis. The goal is to determine current and voltage associated with each circuit element.

Original picture

On the right side author assigned current's direction. I am guessing they used 120A current source to decide on direction. The solution is i_1 = 60A and i_2 = 30A.

I wonder if we can assign current flow differently, using 30A current source. Here is my idea with arrows indicating current flow.

Alternative solution

My solution yields i_1 = 90A and i_2 = 120A. Are both solutions possible? Intuitively, I am guessing that 120A current source is probably will be decisive (so author's original solution is correct), but I cannot find rigourous argument why my alternative solution is wrong. I am also thinking that we can find yet another (3rd) current flow assignment and find another solution.

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  • \$\begingroup\$ Your solution doesn't adhere to KCL: 120 + 90 - 30 + 120 = 300A whereas it should be zero. \$\endgroup\$
    – Peter K.
    Dec 1, 2023 at 17:32

2 Answers 2

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You can assign your current reference directions any way you want. Depending on the reference direction you pick the result may have the opposite sign of the original method, but the magnitudes of the currents should be the same. If they aren't go back and try again. In your example i_1 = -60A and i_2 = -30A.

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  • \$\begingroup\$ s/magnitudes/directions/? \$\endgroup\$ Dec 1, 2023 at 16:22
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The two independent current generators and the two resistors are all in parallel. That is, the four bipoles have only two nodes in common, the upper one and the lower one. The two independent current generators are equivalent to a single generator with current delivered equal to the algebraic sum of each current. The direction of the resulting current is the same as that which has a greater value.

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